Question

George and Barbara will be retiring in four years and would like to buy a lake house. They estimate that they will need $150,000 at the end of four years to buy this house. They want to make four equal annual payments into an account at the end of each year. If they can earn 16% on their money, compounded annually, over the next four years, how much must they invest at the end

Answer 1

$29,606

Step-by-step explanation:

Future Value(FV)=PV×(1+r)^n−1/r

Where,

PV = present value = X

r = rate of interest =16%=16/100= 0.16

n=Number of years = 4

Future Value =FV= $150,000

Future Value(FV)=PV×(1+r)^n−1/r

150,000=X∗(1+0.16)^4−1/0.16

150,000=X*(1.16)^4-1/0.16

150,000=X*1.81063936-1/0.16

150,000=X∗0.81063936^0.16

150,000=X∗5.066496

X=150,000/5.066496

X=29,606.26

Approximately

X=$29,606